When a unital $F$-algebra has all maximal left (right) ideals closed?
Volume 175 / 2006
Studia Mathematica 175 (2006), 279-284
MSC: Primary 46H10.
DOI: 10.4064/sm175-3-6
Abstract
We prove that a real or complex unital $F$-algebra has all maximal left ideals closed if and only if the set of all its invertible elements is open. Consequently, such an algebra also automatically has all maximal right ideals closed.
